A maximum-principle preserving and unconditionally energy-stable linear second-order finite difference scheme for Allen-Cahn equations

DOI10.1016/j.aml.2021.107179OpenAlexW3133729083MaRDI QIDQ2233257

Jundong Feng, Yingcong Zhou, Tianliang Hou

Publication date: 15 October 2021

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2021.107179

zbMATH Keywords

finite difference methoddiscrete maximum principleAllen-Cahn equationleap-frog schemediscrete energy stability

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (10)

Numerical analysis for solving Allen-Cahn equation in 1D and 2D based on higher-order compact structure-preserving difference scheme ⋮ Totally decoupled implicit-explicit linear scheme with corrected energy dissipation law for the phase-field fluid vesicle model ⋮ Effective time step analysis for the Allen–Cahn equation with a high‐order polynomial free energy ⋮ Temporal high-order, unconditionally maximum-principle-preserving integrating factor multi-step methods for Allen-Cahn-type parabolic equations ⋮ Third-order accurate, large time-stepping and maximum-principle-preserving schemes for the Allen-Cahn equation ⋮ An adaptive unconditional maximum principle preserving and energy stability scheme for the space fractional Allen-Cahn equation ⋮ Explicit third-order unconditionally structure-preserving schemes for conservative Allen-Cahn equations ⋮ A conservative Allen-Cahn equation with a curvature-dependent Lagrange multiplier ⋮ Efficiently energy-dissipation-preserving ADI methods for solving two-dimensional nonlinear Allen-Cahn equation ⋮ Numerical analysis of a linear second-order finite difference scheme for space-fractional Allen-Cahn equations

Cites Work

• On the maximum principle preserving schemes for the generalized Allen-Cahn equation
• Barycentric interpolation collocation method based on Crank-Nicolson scheme for the Allen-Cahn equation
• A new second-order maximum-principle preserving finite difference scheme for Allen-Cahn equations with periodic boundary conditions
• Numerical analysis of a stabilized Crank-Nicolson/Adams-Bashforth finite difference scheme for Allen-Cahn equations
• A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations
• Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation
• A spatial fourth-order maximum principle preserving operator splitting scheme for the multi-dimensional fractional Allen-Cahn equation
• Numerical analysis of fully discretized Crank-Nicolson scheme for fractional-in-space Allen-Cahn equations
• Numerical Studies of Discrete Approximations to the Allen–Cahn Equation in the Sharp Interface Limit
• Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
• On Energy Stable, Maximum-Principle Preserving, Second-Order BDF Scheme with Variable Steps for the Allen--Cahn Equation
• Arbitrarily High-Order Exponential Cut-Off Methods for Preserving Maximum Principle of Parabolic Equations

This page was built for publication: A maximum-principle preserving and unconditionally energy-stable linear second-order finite difference scheme for Allen-Cahn equations